(x-1)(-x^3+5x^2)=0

Solution for (x-1)(-x^3+5x^2)=0 equation:

Simplifying
(x + -1)(-1x3 + 5x2) = 0

Reorder the terms:
(-1 + x)(-1x3 + 5x2) = 0

Reorder the terms:
(-1 + x)(5x2 + -1x3) = 0

Multiply (-1 + x) * (5x2 + -1x3)
(-1(5x2 + -1x3) + x(5x2 + -1x3)) = 0
((5x2 * -1 + -1x3 * -1) + x(5x2 + -1x3)) = 0
((-5x2 + 1x3) + x(5x2 + -1x3)) = 0
(-5x2 + 1x3 + (5x2 * x + -1x3 * x)) = 0
(-5x2 + 1x3 + (5x3 + -1x4)) = 0

Combine like terms: 1x3 + 5x3 = 6x3
(-5x2 + 6x3 + -1x4) = 0

Solving
-5x2 + 6x3 + -1x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-5 + 6x + -1x2) = 0

Factor a trinomial.
x2((-5 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 5, 1}